$A$ $B$ $C$ If: $ BC = 2x + 5$, $ AB = 9x + 7$, and $ AC = 34$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 7} + {2x + 5} = {34}$ Combine like terms: $ 11x + 12 = {34}$ Subtract $12$ from both sides: $ 11x = 22$ Divide both sides by $11$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $BC$ $ BC = 2({2}) + 5$ Simplify: $ {BC = 4 + 5}$ Simplify to find ${BC}$ : $ {BC = 9}$